Stages in the History of Algebra with Implications for Teaching

In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra. Commentary from a Mathematics Educator Bill Barton. See also the last page. Commentary from a Mathematics Educator     

Developing a database of authoring system software

AuthorBase, a working prototype database of authoring system software, was developed as part of a study of authoring software conducted by the National Library of Medicine. In this article, the authors discuss development issues ranging from the scope of the database to what information to document. The prototype demonstrates that records of reasonable integrity can be derived from vendor-supplied information. However, users should understand that the database is only a starting point in searching for authoring software and a resource for becoming generally familiar with the technology.     

Homophobia in Counselling Practice

Current attitudes of counselling practitioners towards sexual and gender differences raise the possibility that minority clients may experience re-traumatisation due to in-session expressions of therapist homophobia. This paper explores these issues through a qualitative study that examines client and counsellor narratives on homophobia in counselling. The results describe specific examples of homophobic behaviour by counsellors. While individual examples might appear mundane on the surface, the frameworks they invoke and their pervasiveness constitutes a considerable threat to the counselling relationship. The paper argues that homophobia in counselling practice is a significant issue that requires sensitive, critical and applied analysis that redirects therapeutic efforts in the future.     

Factors Influencing Positive Interactions Across Race for African American, Asian American, Latino, and White College Students

This study explores the various factors that promote positive interactions across race for African American, Asian American, Latino, and White college students. A longitudinal survey was administered to all incoming students at nine public institutions (with a follow-up survey given at the end of their second year), examining activities related to cross-racial interaction and outcomes. This knowledge will be useful for college administrators, institutional researchers, and faculty as they work to meet the challenge of preparing students for a pluralistic society. The results of this study begin to delineate the conditions under which positive intergroup relations can be fostered in college and the key factors that inhibit or restrain the benefits such interactions bring to the development of students for a diverse workplace and pluralistic democracy.     

The value of theories for counseling practitioners

The emergence of counseling as a recognized helping profession has led to the introduction of higher standards for counselor education. Emphasis has been placed on a balance between theoretical erudition and practical training. Some counseling practitioners, however, minimize the value of theoretical knowledge and doubt its importance for professional effectiveness. This article challenges such views and points out that counselors cannot remain true professionals unless they undergird their work by adequate theoretical insights. Theories help counselors understand the dynamics of human behavior and choose therapeutic approaches appropriate to specific clients and situations. Psychological theories come alive in the counselor's mind if they are seen as extensions of life experiences of various theorists. To document this reality, the article presents several examples of well-known psycholoical theorists. Counseling practitioners are then encouraged to form, on the basis of existing theories, an operational framework consistent with their own experiences and values.     

The effect of frequency of testing upon the measurement of achievement in an intensive time-series design

Progress in the development of an intensive time-series design for use in classroom situations has raised several questions regarding the validity of the data obtained. One such question is related to the effect of frequency of testing upon the data. This study was designed to determine the presence of such an effect. Use of the design with eighth grade students studying a unit on crustal evolution indicated that the frequency of data collection did not adversely affect student attitudes toward the science class nor did it have any measurable effect upon class achievement data. The results of a previous study were also replicated, giving increased confidence in the validity of the data yielded by the intensive time-series design as used in these studies.     

Shorter notices

Thomas, Mike and Thomas, Sally (1981) On Our Own TWO Feet, Books 6 to 8 (Settling In, Safe and Secure, Around and About). Horton, M. (1980) The Second Reading and Writing Book. A Handbook for Teachers and Parents to Use with Children. Edwards Reading Test (1980) Heinemann Educational Books.     

A Model of Technology Incidental Learning Effects

Educational Psychology Review - Increases in technology use, among youth and adults, are concerning given the volume of information produced and disseminated in the modern world. Conceptual models...     

Understanding our link to the Great Apes—the 2003 Benjamin Franklin Medal in Life Sciences awarded to Jane Goodall

Jane Goodall is the recipient of the 2003 Benjamin Franklin Medal in Life Sciences for her long-term scientific studies of chimpanzee behavior. Not only were her studies the first of their kind, her meticulous behavioral recordings led to major changes in our understanding of the social links that exist between ourselves and our closest living relative, the chimpanzee. In discussing the importance of Dr. Goodall's work, Stephen Jay Gould (the late Alexander Agassiz Professor of Zoology at Harvard University) said ... “Science gains enormous power in replications of observations, but Homo sapiens is a single species and we can never know, by studying ourselves alone, whether important aspects of our behaviors and mental capacities reflect an ancestral evolutionary heritage (transmogrified through our uniquely evolved intelligence and its social correlates), or new features evolved or socially acquired only by our lineage. Chimpanzees are the best natural experiment we will ever have for exploring this central question, for chimps are our closest genealogical cousins and therefore hold more of our common evolutionary heritage than any other species can. Chimpanzees are not so much the shadow of man as our mirror, only slightly blurred by the mists of time”.